Preface xv
Chapter 1. Basic Concepts 1
1.1. Introduction 1
1.2. Definition of terms 1
1.2.1. Risk 1
1.2.2. Time definitions 2
1.2.3. Failures and repairs 4
1.2.4. IEC 61508 terms 8
1.3. Definition of parameters 10
1.3.1. Reliability 10
1.3.2. Maintainability 12
1.3.3. Availability and production availability 12
1.3.4. Dependability 13
1.3.5. Definitions used by maintenance engineers 13
1.3.6. Definitions used in the refinery industry 14
1.4. The exponential law/the constant failure rate 14
1.4.1. Reliability 14
1.4.2. Validity 15
1.4.3. Oil and gas industry 16
1.5. The bathtub curve 16
1.5.1. Meaning 16
1.5.2. Useful life and mission life 18
1.5.3. Validity 18
1.5.4. Oil and gas industry 18
Chapter 2. Mathematics for Reliability 21
2.1. Introduction 21
2.2. Basis of probability and statistics 22
2.2.1. Boolean algebra 22
2.2.2. Probability relations 22
2.2.3. Probability distributions 24
2.2.4. Characteristics of probability distributions 24
2.2.5. Families and conjugates 26
2.3. Formulae and theorems 27
2.3.1. Combinatorial analysis 27
2.3.2. Central limit theorem 28
2.3.3. Chebyshevâs inequality 28
2.3.4. Laws of large numbers 28
2.3.5. Supporting functions and distributions 29
2.3.6. Bayesâ theorem 30
2.4. Useful discrete probability distributions 32
2.4.1. Binomial distribution 33
2.4.2. Poisson distribution. 33
2.5. Useful continuous probability distributions 35
2.5.1. Exponential distribution 35
2.5.2. Uniform distribution 36
2.5.3. Triangular distribution 37
2.5.4. Normal distribution 38
2.5.5. Log-normal distribution 40
2.5.6. Weibull distribution 43
2.5.7. Gamma distribution 44
2.5.8. Beta distribution 45
2.5.9. Chi-squared distribution 46
2.5.10. Fisher-Snedecor distribution 46
2.6. Statistical estimates 47
2.6.1. Estimates 47
2.6.2. Calculation of point estimate 47
2.6.3. Calculation of confidence interval 50
2.6.4. Heterogeneous samples 52
2.6.5. Implementation 53
2.7. Fitting of failure distribution 53
2.7.1. Principle 53
2.7.2. Median rank method 54
2.7.3. Implementation 55
2.8. Hypothesis testing 57
2.8.1. Principle 57
2.8.2. Existing tests. 58
2.8.3. Implementation 58
2.9. Bayesian reliability 60
2.9.1. Definition 60
2.9.2. Use of Bayesâ theorem 61
2.9.3. Bayesian inference 61
2.9.4. Selection of the prior probability distribution 62
2.9.5. Determination of the posterior probability distribution 62
2.9.6. Bayesian credibility interval 64
2.10. Extreme value probability distributions 65
2.10.1. Meaning. 65
2.10.2. The three extreme value probability distributions 65
2.10.3. Use in the industry 66
Chapter 3. Assessment of Standard Systems 67
3.1. Introduction 67
3.2. Single item 67
3.2.1. Availability 68
3.2.2. Number of failures 69
3.3. System reliability 70
3.3.1. Series systems 70
3.3.2. Parallel systems 72
3.4. Specific architectures 73
3.4.1. Method of analysis 73
3.4.2. Redundant item system 74
3.5. On-guard items 76
3.5.1. Unrevealed failures 76
3.5.2. Full formula 77
3.5.3. Optimum proof test duration 79
Chapter 4. Classic Methods 81
4.1. Introduction 81
4.2. Failure Mode and Effects Analysis 81
4.2.1. Conventional Failure Mode and Effects Analysis/Failure Mode,Effects and Criticality Analysis 81
4.2.2. Functional/hardware FMEA 84
4.2.3. Case study 84
4.3. Fault trees 89
4.3.1. Conventional fault trees 89
4.3.2. Fault tree extensions 93
4.3.3. Facilities provided by software packages 94
4.3.4. Case study 94
4.4. Reliability block diagrams 98
4.4.1. Conventional RBDs 98
4.4.2. RBD extension 102
4.4.3. Facilities provided by software packages 103
4.4.4. Case study 103
4.5. Monte Carlo method 104
4.5.1. Principle 104
4.5.2. Use for production availability and reliability 106
4.5.3. How many runs are enough? 107
Chapter 5. Petri Net Method 109
5.1. Introduction 109
5.2. Petri nets 110
5.2.1. Definition 110
5.2.2. Mathematical properties 111
5.2.3. Petri net construction 112
5.2.4. GRAFCET 117
5.3. IEC 62551 extensions 117
5.3.1. Extensions to structure 117
5.3.2. Modified execution rules 120
5.4. Additional extensions 121
5.4.1. Extensions to structure 121
5.4.2. Modified execution rules 122
5.5. Facilities provided by software packages 123
5.5.1. Additional extensions to structure 123
5.5.2. Modified execution rules 123
5.5.3. Petri net processing 123
5.5.4. Results 123
5.6. Petri net construction 124
5.6.1. Petri net modeling 124
5.6.2. Minimizing the risk of error input 124
5.6.3. Petri net checking 124
5.6.4. Petri net validation 125
5.7. Case study 125
5.7.1. System description 125
5.7.2. Petri net model 126
Chapter 6. Sources of Reliability Data 133
6.1. Introduction 133
6.2. The OREDA project 133
6.2.1. History 133
6.2.2. Project management and organization 135
6.2.3. Description of OREDA 2015 handbooks 135
6.2.4. Use of the data tables 137
6.2.5. Use of the additional tables 141
6.2.6. Reliability database and data analysis software 143
6.2.7. Data collection software 144
6.3. The PDS handbook 144
6.3.1. History 144
6.3.2. Description of the handbook 145
6.3.3. Use of the handbook 145
6.4. Reliability Analysis Center/Reliability Information Analysis Center publications 145
6.4.1. History 145
6.4.2. Non-electronic Part Reliability Data handbook 146
6.4.3. FMD 146
6.4.4. NONOP 146
6.4.5. Use of the publications 146
6.5. Other publications 147
6.5.1. EXIDA handbooks 147
6.5.2. Electrical items 147
6.5.3. Pipelines 148
6.5.4. Flexibles 149
6.5.5. Miscellaneous 149
6.6. Missing information 150
Chapter 7. Use of Reliability Test and Field Data 151
7.1. Introduction 151
7.2. Reliability test data 151
7.2.1. Principle 151
7.2.2. Test organization 152
7.2.3. Assessment of failure rate 152
7.3. Field data 154
7.3.1. Principle 154
7.3.2. Data collection organization 155
7.3.3. Assessment of failure rate 155
7.3.4. Assessment of probability to fail upon demand 156
7.3.5. Assessment of MRT 156
7.3.6. Case study 156
7.4. Accelerated tests 157
7.4.1. Principle 157
7.4.2. Example 158
7.4.3. Highly accelerated tests 159
7.5. Reliability growth 159
7.5.1. Principle 159
7.5.2. Main models 159
Chapter 8. Use of Expert Judgment. 163
8.1. Introduction 163
8.2. Basis 164
8.2.1. Definitions 164
8.2.2. Protocol for expert elicitation 164
8.2.3. Role of the facilitator 165
8.3. Characteristics of the experts 166
8.3.1. Definition 166
8.3.2. Selection 166
8.3.3. Biases 167
8.3.4. Expert weighting 168
8.3.5. Expert dependence 169
8.3.6. Aggregation of judgments 169
8.4. Use of questionnaires 169
8.4.1. Conditions of use 169
8.4.2. The Delphi method 170
8.4.3. Case study 171
8.5. Use of interactive group 173
8.5.1. Number of experts 173
8.5.2. Procedure. 173
8.6. Use of individual interviews 174
8.6.1. Conditions of use 174
8.6.2. Case study 174
8.7. Bayesian aggregation of judgment 175
8.7.1. Form of information provided by experts 175
8.7.2. Assessment of failure rate (or MTBF) 176
8.7.3. Assessment of probability of failure upon demand 177
8.8. Validity of expert judgment 177
Chapter 9. Supporting Topics 179
9.1. Introduction 179
9.2. Common cause failures 179
9.2.1. Introduction 179
9.2.2. Definition 180
9.2.3. Defenses against CCF 181
9.2.4. CCF modeling with the beta-factor method 182
9.2.5. CCF modeling with the shock method 185
9.2.6. Extension of the beta-factor model: the PDS method 188
9.2.7. Field data 189
9.2.8. Impact of CCF on system reliability 190
9.2.9. Impact of testing policy on CCF 191
9.2.10. Impact of CCF on system production availability 194
9.2.11. Benchmark on CCF assessment 194
9.3. Mechanical reliability 195
9.3.1. Characteristics 195
9.3.2. Stress-strength interference 195
9.3.3. Empirical reliability relationships 197
9.3.4. Comparison with system (constant failure rate) approach 199
9.4. Reliability of electronic items 199
9.4.1. Characteristics 199
9.4.2. MIL-HDBK-217 200
9.4.3. UTE-C-80811 201
9.4.4. Other reliability data books 201
9.4.5. EPRD 203
9.4.6. Effect of dormancy period 203
9.4.7. Common cause failures 203
9.4.8. Comparison of previsions 204
9.4.9. Use in the oil and gas industry 205
9.5. Human reliability 205
9.5.1. Human factors 205
9.5.2. Human reliability in the nuclear industry 205
9.5.3. Evaluation of HRA techniques 206
9.5.4. Human reliability in the oil and gas industry 206
Chapter 10. System Reliability Assessment 209
10.1. Introduction 209
10.2. Definition of reliability target 209
10.2.1. Absolute reliability target 209
10.2.2. Risk target 210
10.3. Methodology of system reliability study 211
10.3.1. Overall description 211
10.3.2. Step 1: system analysis 212
10.3.3. Step 2: qualitative analysis. 212
10.3.4. Step 3: quantitative data selection 212
10.3.5. Step 4: system reliability modeling 214
10.3.6. Step 5: synthesis 214
10.4. SIL studies 214
10.4.1. Introduction 214
10.4.2. SIL assignment 214
10.4.3. SIL demonstration 217
10.5. Description of the case study 217
10.5.1. Origin of the risk 217
10.5.2. Description of the standard SIF 219
10.5.3. Risk assessment 219
10.6. System analysis 220
10.6.1. Description of HIPS functioning 220
10.7. Qualitative analysis 221
10.7.1. FMEA 221
10.7.2. CCF analysis 223
10.8. Quantitative data selection 225
10.8.1. Selection of reliability data 225
10.8.2. Collection of proof test data 225
10.8.3. CCF quantification 226
10.9. System reliability modeling 226
10.9.1. Building of system reliability model 226
10.9.2. System reliability calculation 226
10.10. Synthesis 232
10.10.1. Conclusions 232
10.10.2. Recommendations 233
10.11. Validity of system reliability assessments 234
10.11.1. Reports 234
10.11.2. Conclusions 234
Chapter 11. Production Availability Assessment 235
11.1. Introduction 235
11.2. Definition of production availability target 235
11.2.1. Absolute production availability target 235
11.2.2. Economic target 235
11.3. Methodology 236
11.3.1. Events considered in production availability assessments 236
11.3.2. Overall description 236
11.3.3. Step 1: system analysis 238
11.3.4. Step 2: quantitative data selection 238
11.3.5. Step 3: production availability assessment 238
11.3.6. Step 4: synthesis 238
11.4. System analysis 239
11.4.1. Determination of system running modes 239
11.4.2. Item failure analysis 242
11.5. Quantitative data selection 244
11.5.1. Selection of reliability data 244
11.5.2. Collection of operational data 245
11.6. Production availability assessment 246
11.6.1. Building of production availability model 246
11.6.2. Production availability calculations 246
11.7. Synthesis 248
11.7.1. Main results 248
11.7.2. Additional economic parameters 249
11.7.3. Flared gas 251
11.7.4. Other results 253
11.7.5. Recommendations 256
11.8. Uncertainty on the reliability parameters 256
11.9. Validity of production availability assessments 257
Chapter 12. Management of Production
Availability and Reliability 259
12.1. Introduction 259
12.2. Principles of dependability management 260
12.2.1. Dependability property management 260
12.2.2. Phasing of the management 260
12.2.3. Lifecycle costing and dependability 261
12.3. Technical specifications 262
12.3.1. Contents. 262
12.3.2. Reliability specification 262
12.3.3. Production availability specification 263
12.4. Reliability and production availability program 264
12.4.1. Contents. 264
12.4.2. Reliability program 266
12.4.3. Production availability program 267
12.5. Validation of system reliability 267
12.5.1. Reliability data collection 267
12.5.2. Random failures 268
12.5.3. Common cause failures 268
12.6. Validation of production availability 268
12.6.1. Useful life 268
12.6.2. Reliability data 269
12.6.3. Production data 269
12.6.4. Use of production availability model 269
Appendices 271
Appendix 1. Notations and Abbreviations 273
Appendix 2. Markov Chain 283
Appendix 3. Comparison of Modeling Methods 293
Appendix 4. Solutions of Exercises. 301
Bibliography 315
Index 323
